Fallen Heroes Family Act of 2013 - Amends the Immigration and Nationality Act to include as a nonimmigrant alien an alien who is the parent of a child who: (1) is a U.S. citizen; (2) was born outside the United States and its outlying possessions; and (3) had a natural parent who served honorably in an active-duty status in the U.S. Armed Forces and died on or after September 11, 2001, from an injury or disease incurred in or aggravated by that service.

Defines "parent" to include a legal guardian or other person standing in loco parentis for purposes of: (1) such nonimmigrant alien; and (2) immediate relative status with respect to aliens who are not subject to direct numerical limitations.

Sets forth related conditions concerning: (1) employment, (2) period of authorized admission, and (3) number of aliens to be admitted for each such child.